Various types of high-performance electronic devices are being developed that use heterojunctions in semiconductor devices therein made of compounds such as GaAs. Since the characteristics of these high-performance electronic devices are influenced by the quality of crystallinity, high quality crystal thin films are desired. The need for lattice matching at the heterointerfaces in thin film crystal growth of GaAs-based devices leads to the selection of wafers made of GaAs or of materials such as Ge whose lattice constant is very close to that of GaAs.
Non-Patent Document 1 discloses a technique for forming a high quality Ge epitaxial growth layer (sometimes referred to hereinafter as a “Ge epilayer”) on an Si wafer. With this technique, the Ge epilayer is formed in a limited region on the Si wafer, and cyclic thermal annealing is then performed on the Ge epilayer to achieve an average dislocation density of 2.3×106 cm−2.    Non-Patent Document 1: Hsin-Chiao Luau et. al., “High-quality Ge Epilayers on Si with Low Threading-dislocation Densities” APPLIED PHYSICS LETTERS, Volume 75, No. 19, Nov. 8, 1999.